Today I learned… in code

A lot happens between "Hello World" and "Supreme Master Programmer". Here, we share little discoveries made along the way. The more frustrating something was, the more likely it is to end up here on this site!

How to convert a 4-byte hexadecimal sequence in a little-endian architecture into decimal

Here is my technique for solving the problem of converting a 4-byte hexadecimal sequence in a little-endian architecture into decimal.

This may seem rather niche but it was a surprisingly large part of Week 5 in my CS271 class. The class’s materials and extra help I found around the web seemed to go off on tangents that were interesting but unrelated to solving this kind of problem quickly, and all I really wanted was a simple step-by-step guide I could use on exams.

The four-byte sequence 0x86 0x65 0x53 0x82 stored in consecutive memory cells in a little-endian architecture represents ___________ (decimal) when interpreted as a 32-bit signed integer.

From reading this, we know:

it’s little-endian, so we are going to reverse the order of the bits

our result will be signed

Step 1: Reverse the bytes

Take the bits in blocks of two and work right to left.

0x86 0x65 0x53 0x82 becomes 0x82536586

Step 2: Look at the most significant bit and determine if there will be a negative result

0x82536586 <-- that's this dude in red here

The most significant bit here contains an 8.

We know that in hex a most-significant bit of 7 or more means we are looking at a negative number. (If this were a positive number, ie: the most significant bit is between 0 and 6, then skip ahead to Step 4.)

Step 3: Since we are working with a negative number, flip the bits (subtract our hex sequence from FFFFFFFF) and add 1

FFFFFFFF
- 82536586
7DAC9A79

Add one to the result:

7DAC9A79
+1
7DAC9A7A

The result is the hex sequence we will use for the next step.

7DAC9A7A

Step 4: Multiply each term by 16 raised to a power

To convert a hex value into a decimal value, we multiply each “position” in the hex sequence by 16 raised to a power. Working from right to left, we know that furthest-right position is 16^0 (so, just a 1). The second-from-right position is 16^1 (so, just a 16). The third-from-right position is 16^2, and so on.

Some final notes

Be sure to observe whether the problem expects a signed decimal result or an unsigned decimal result. If the problem is asking for unsigned, you can skip the FFFFFFFF subtraction step entirely, even if the most significant bit is 7 or higher.

Remember that when working with a signed hexadecimal number, you look at the most significant bit to determine if it’s negative or positive.

0-7 = positive

8-F = negative

If you had to do the flipping step, don’t forget to put that negative sign onto your final answer!